Palindrome Formation from Character Frequencies

Given a set of characters and their frequencies, determine whether it is possible to rearrange them to form a palindrome.

A string is a palindrome if it reads the same forwards and backwards. In order for a set of characters to form a palindrome, at most one character can have an odd frequency. Mathematically, if we define \(oddCount\) as the number of characters whose frequency is odd, then the condition to form a palindrome is:

\(oddCount \le 1\)

You are given the number of distinct characters followed by each character and its frequency. Output True if a palindromic permutation exists, and False otherwise.

inputFormat

The input is given via stdin and consists of:

1. An integer N representing the number of distinct characters.
2. N lines, each containing a character and an integer frequency, separated by a space.

For example:

3
 a 2
 b 3
 c 2

outputFormat

Print a single line to stdout containing True if it is possible to form a palindromic string from the given frequencies, or False otherwise.

## sample

3
a 2
b 2
c 2

True

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